A recent line of research, initiated in the work by Weitz et al. [1]}, has attracted a great attention as it proposes a new way to model the reciprocal dependence of the payoffs on the environment and vice versa, taking into account the enhancement and degradation effects on the environmental resource. This is done through a direct dependence of the payoff matrix on the environment, giving rise to interesting system dynamics characterised by oscillatory behaviours and equilibria on the boundary of the phase space. The resulting oscillations correspond to closed periodic orbits. Limit cycles have been observed also when a time-scale difference between the game and the environment dynamics is considered [2]}.
